Theory and Behavious in Reverse Auctions

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e-Sourcing in Procurement: Theory and Behavior in ReverseAuctions with Non-Competitive Contracts

Richard Engelbrecht-Wiggans

College of BusinessUniversity of IllinoisChampaign, IL 61820

[email protected]

Elena Katok

Smeal College of BusinessPenn State University

University Park, PA, [email protected]

October 22 2004

AbstractOne of the goals of procurement is to establish a fair price while affording the buyer someflexibility in selecting the suppliers to deal with. Reverse auctions do not have this flexibility, because it is the auction rules and not the buyer that determine the winner. But an importantadvantage of having this flexibility is that it allows buyers and suppliers to establish long-termrelationships. This is one of the reasons that buyers often combine non-competitive purchasingwith auctions. We find that in theory such hybrid mechanisms that remove some suppliers and acorresponding amount of demand from the auction market increase competition and make buyers

better off as long as suppliers are willing to accept non-competitive contracts. And it turns outthat suppliers often do because under a wide variety of conditions these contracts have a positiveexpected profit. Our theory relies on two behavioral assumptions: (1) bidders in a multi-unituniform-price reverse auction will follow the dominant strategy of bidding truthfully, and (2) thesuppliers who have been removed from the market will accept non-competitive contracts thathave a positive expected profit. Our experiment demonstrates that bidders in the auction behavevery close to following the dominant strategy regardless of whether this auction is a stand-aloneor a part of a hybrid mechanism. We also find that suppliers accept non-competitive contractssufficiently often (although not always) to make the hybrid mechanism outperform the reverseauction in the laboratory as well as in theory.

JEL Classification Numbers: C72, D83, D44, C91Keywords: Multi-Unit Auctions, Experimental Economics, Strategic Procurement

The authors gratefully acknowledge the support from the National Science Foundation


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1. Introduction

With the growth of the internet, e-Sourcing, has become an important tool for

procurement. E-Sourcing is a catch-all term that refers to the use of internet-enabled applications

and decision support tools that facilitate competitive and collaborative interactions among buyers

and suppliers through the use of online negotiations, reverse (decreasing bid) auctions, and other

related tools. According to a September 2002 report by the Aberdeen Group (Aberdeen Group,

2002), e-Sourcing revenues increased from $820 million in 2001 to $1.14 billion in 2002, and are

projected to increase to $3.13 billion by 2005.

The use of auctions in e-Sourcing may save buyers considerable amounts of money.

Such on-line auctions received much attention in the press when General Electric (GE) claimed

savings of over $600 million and net savings of over 8% in 2001 by using SourceBid, a reverse

auction tool and a part of GEs Global Exchange Network (GEN)1. The U.S. General Services

Administration attributed savings of 12% to 48% to the use of auctions (Sawhney 2003), and

FreeMarkets, one of the leading on-line auction software providers, reported that its customers

saved approximately 20% on over $30 billion in purchases between 1995 and 2001.

However, auctions may not be delivering quite as much savings as hoped. The Aberdeen

Group 2002 reports that 60% of end-users were unable to realize fully the savings that they had

negotiated using e-Sourcing technologies, primarily due to the lack of effective communication

of negotiated terms. Emiliani and Stec 2001 argue that not only do auctions rarely deliver

savings as great as advertised, but also, they inflict damage on the long-term buyer-supplier

relationships by inhibiting collaboration2.

The importance of long-term relationships in procurement has been well established (see

for example Monczka, Trent and Handfield 2005), and auctions as such are not conducive to

promoting long-term relationships. But we should not be too quick to dismiss auctionsthey

1 According to a case study written by GEs Global Exchange Services (Global Exchange Services 2003), GEsGlobal Exchange Network is used by about 35,000 suppliers and handles over 10,000 e-invoicing enquiries per day.Approximately 37,000 reverse auctions, worth about $28.6 billion, have been conducted between 2000 and the 2ndquarter of 2002, generating $680 million in savings in 2000-01 and additional $900 million in savings projected for2002.2 Another common criticism of auctions is that they squeeze suppliers on price thus putting small suppliers at adisadvantage. But, it should be noted that auctions also give small suppliers access to a large market that they maynot have had access to otherwise.

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have many benefits. Because auctions are visible, structured, and have clear rules, they make the

procurement process transparent and, at least in theory, they yield a fair market price. Without

this, the procurement process can become disastrously flawed. For example, one recent,

notorious illustration of what can happen without competitive bidding is the $7 billion no-bid

contract awarded by the US Army to Kellogg, Brown & Root (KBR), a Halliburton subsidiary,

in March of 20033.

So, let us look at auctions a bit more closely. Auctions introduce market competition into

the procurement process, and this competition does put a downward pressure on price. However,

auctions also determine who wins versus loses. In the case of e-Sourcing, this second function of

auctions seems to be the source of the problem. Specifically, if a buyer conducts a sequence of

auctions over time, each auction may result in different suppliers winning. Such a turn-over in

suppliers does not facilitate long term relationships between a buyer and that buyers suppliers.

Our work is motivated by the desire to create mechanisms that preserve benefits of

auctions but limit their detrimental effect on long-term relationships. We investigate a

mechanism that combines auctions with non-competitive contracts; an auction among some of

the suppliers sets the price and the buyer contracts non-competitively with other suppliers to

provide goods at whatever price the auction sets. This hybrid mechanism retains the price setting

benefits of auctions; the auction component of the mechanism provides a transparent process for

injecting market competition into the procurement process. However, the buyer retains some

control over deciding which suppliers to deal with (in other words, this decision is not part of the

mechanism). The buyer could repeatedly contract with same non-competitive suppliers, thus

retaining the long-term relationships with those suppliers.

The understanding of mechanisms that combine auctions and negotiationsthe type of

mechanisms most often used in practiceis quite limited. Jap 2002 provides a review of issues

3 This contract, know as Restore Iraqi Oil (RIO), was a 2 year cost plus contract worth up to $7 billion to KBR forrebuilding Iraqs oil infrastructure and extinguishing oil well fires. The no-bid contract caused such outrage inCongress and directed spotlight on Halliburton and the Vice President Dick Cheney, who served as the HalliburtonCEO from 1995 through 2001, that the contract was subsequently cancelled and opened up for bid. Ultimately, thebulk of the contract was still awarded to KBR, and the balance to a joint venture of the California-based ParsonsCorp. and the Australian firm Worley Group Ltd (Halliburton Watch 2004).

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in on-line reverse auctions used for procurement, including how these auctions differ from

standard physical auctions (they typically have lower transaction costs and allow for bidder

anonymity), and how they differ from auctions in the theoretical auction literature. There are

two fundamental differences between on-line reverse auctions prevalent in practice and the

models of auctions in the theory literature. The first difference is that in practice the value of

products in procurement settings cannot be reduced to the single dimension of price. This leads

to the second differencethe vast majority of auctions actually used in practice do not determine

winners. In other words, the buyer (the auctioneer) does not commit to awarding the contract to

the lowest bidder, but instead reserves the right to select the winner from a set of bidders. This

type of mechanism has not been analyzed either theoretically or in the laboratory, but Jap 2002

reports on some empirical findings from interviewing buyers and sellers.

Reverse auctions are usually a part of e-Sourcing tool kits, but they are not used

exclusively, and although prevalent, they do not constitute the majority of e-Sourcing

transactions. In addition to auctions, e-Sourcing applications typically provide platforms for on-

line negotiations, such as request for quotes (FRQ), and request for proposals (RFP). The

question of which is better (auctions or negotiations) is a complicated one. Bulow and

Klemperer 1996, for example, show that if the seller is able to attract just one more serious

bidder to the auction, then he can make higher expected revenue from an auction than from a

negotiation. The Bulow and Klemperer model is stylized, and the example they used is selling a

company. Although a company is a complex object, the contract for selling it can be easily

reduced to a single dimensionprice per sharea setting most conducive to auctions.

Bajari et al. 2003 compare auctions and negotiations in a context of contracts that cannot

be easily reduced to a single dimension. They examine private sector building contracts awarded

in Northern California between 1995 and 2000 and find that auctions perform poorly when

contracts are complex, specifications are incomplete, or the number of bidders is small. They

also find that auctions tend to suppress communication between buyers and sellers.

Salmon and Wilson 2004 investigate a setting with two units in which the seller starts out

by auctioning off one unit using an ascending-price auction, and then negotiating with the price-

setting bidder for the remaining unit. The negotiation process is modeled as the Ultimatum

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game4. Salmon and Wilson 2004 find that since the losing bidder does not wish to reveal his true

value, truthful bidding is not an equilibrium for the auction, and actually the only equilibria that

exist are in mixed strategies. The authors find that the hybrid auction/negotiation mechanism is

able to raise more money than the benchmark mechanism that consists of two sequential

ascending-bid auctions.

Mechanisms that most closely resemble those used by e-Sourcing applications are ones

that combine auctions with some form of negotiations. Jap 2002 reports that suppliers generally

do not like reverse auctions because they feel the visibility of their prices to competitors

erodes their bargaining power. (pg. 521). They feel that the computer interface prevents them

from informing buyers about non-price attributes of their products, and thus causes their products

to become commoditized. And they also fear losing control and bidding too low in the heat of

the moment. In fact, according to Jap 2002, suppliers take the use of on-line reverse auctions by

the buyers as a signal about the nature of their relationship, and they respond to this signal:

If suppliers believe that the use of on-line reverse auctions signals a movement towards market-oriented, arms-length relations, then suppliers will act accordingly. As suppliers believe that buyers are increasingly short-term oriented and concerned about their own gains, then they too may respond in kind. However, if the buyersignals that the on-line auctions are a rare occurrence, used as a stepping stone to a long-term, mutuallybeneficial financial arrangement, then suppliers will be more motivated to become mutually oriented and mayrespond more competitively in light of the long-term gains. (pg. 521).

In other words, an occasional use of an auction by the buyer is (correctly) interpreted by

suppliers as a way to keep them honest rather than as a signal that the buyer is ready to

abandon the relationship. Therefore, suppliers are more likely to bid aggressively in such

auctions, as a signal of good faith (see Goeree 2003 for a model of auctions with an aftermarket)

because their own low bid signals a commitment to the relationship. But if buyers use auctions

all the time, then suppliers lose the incentive to signal their commitment, and simply compete on

price (or choose to not participate in the auctions and take their business elsewhere).

The work most closely related to ours is Engelbrecht-Wiggans 1996, who presents a

model of a mechanism that combines a multi-unit auction with some non-competitive contracts.

In this model, suppliers have the option to commit to supply the units at a price to be determined

by the auction. Doing so saves the supplier some auction participation fee (but typically results

in a less desirable price.) Under a variety of conditions, even when bidders are homogeneous, at

4 In the Ultimatum game the proposer makes a take-it-or-leave-it offer to the responder. If the responder rejects theoffer, then both players earn zero (or their outside option).

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equilibrium some will voluntarily choose the non-competitive contract while others will choose

to bid in the auction and the auctioneer benefits from having allowed non-competitive sales.

Our study is a step towards gaining analytical and empirical insight into hybrid

mechanisms that combine auctions with non-competitive contracts. We develop a model of a

simple hybrid environment that combines an English auction with non-competitive contracts.

We find that in theory this mechanism yields lowers costs to the buyer than a pure auction

mechanism while still generating positive profits for suppliers. We then proceed to compare the

two mechanisms in the laboratory, and find our theoretical benchmarks to be quite accurate. In

section 2 we present our model and theoretical benchmarks. We describe the experimental

design and related hypothesis in section 3, present results in section 4, and offer conclusions,

managerial insights, and directions for future research in section 5.

2. Theory

In this section we develop the basic model and derive key theoretical results. We will

start by describing the general structure of the model, and then precisely define the two

mechanisms of interest. We then examine implications for the buyer, for the suppliers and for

efficiency. These theoretical predictions serve as benchmarks for the laboratory experiment.

Imagine a buyer who needs to procure Q units of some commodity. There are N

suppliers from whom the buyer can try to obtain units. Each supplier i (i = 1, 2, N) can

provide a single unit, knows his cost Ci of doing so, and has some say in whether or not he

supplies a unit. If too few suppliers agree to provide units, then the buyer incurs some fixed cost

for each of the remaining units; this cost may be interpreted in a variety of ways,

including as the cost to the buyer of unsatisfied demand, as the cost of units from some unlimited

backup supply source, or as the cost to the buyer of manufacturing the units in-house.

o iC C i

One mechanism for determining which suppliers will provide units is a descending-bid

(reverse) uniform-price auction. Consider the following stylized version of this auction: the

buyer starts by offering a price of per unit and then reduces the price continuously; letPoC t

denote the price at time t. At any point in time a buyer can drop out of the auction, and once out

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cannot bid again. The price continues to decrease until there are exactly Q suppliers left willing

to provide a unit5.

Suppliers have the dominant strategy of dropping out of the auction at a point wherePt =

Ci. At this point, the auction price is exactly the suppliers cost, and the final auction price will

be exactly equal to cost to the losing supplier who was the last to drop out. Our theory presumes

that suppliers use this dominant bidding strategy.

The idea behind using an auction is that it establishes a competitive price. In order for

there to be any competition in the auction, there must be at least one supplier who loses in the

sense of not supplying a unit to the buyer. Therefore, let us assume thatN 2 and that 1 QN-

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Furthermore, intuitively, the more suppliers that must losei.e., the greater the excess

supplythe greater the competition will be, and the lower the expected cost will be to the buyer.

So, let us examine how the buyer might increase competition.

One possibility is for the buyer to find additional potential suppliers, thereby increasingN

and the excess supply; we presume that the buyer has already done so and that Ncan not be

increased any further. Another possibility is for the buyer to reduce the number of units to be

procured through the auction. This also increases the excess supply in the auction, but leaves the

buyer with fewer than Q units. Our model already allows the buyer to make up for any shortfall

at a cost ofC0 per unit. But can the buyer do better than this?

Consider the following extension to the auction. Suppose that prior to the auction the

buyer approaches some of the supplier and offers them an opportunity to commit to providing

the units at a price to be established later, by the auction7. More specifically, let Mdenote the

number of suppliers to whom the buyer makes this offer. Those who turn down this offer are not

allowed to participate in the auction; the auction will have the otherN-Msuppliers competing for

5 If the price decreases in discrete steps and/or suppliers have positive probability of having exactly the same cost,then there will be a positive probability that more than one supplier drops out at the same time. Our theoryapproximates reality by assuming a continuous price decrease and continuous value distributions. This assures thatthere is zero probability of two or more suppliers dropping out at the same time. In practice, if multiple suppliers

drop out simultaneously, and this causes the supply to become strictly less than demand, the units could be allocatedto all the suppliers who stayed in and randomly among the suppliers who dropped out last.6 These, and subsequent, technical restrictions will hold in our experimental settings.7 In the Engelbrecht-Wiggans, 1996,model, there is a cost to participate in the auction and individuals could decidewhether or not to compete in the auction or take the non-competitive route; the number of non-competitive sales wasendogenously determined. In contrast, in the proposed model, there is no cost of participating in the auction. As aresult, suppliers would prefer to participate in the auction rather than take the non-competitive route. So the modelassumes that the buyer can exogenously set the number of non-competitive sales M, and these Msuppliers haveoption of turning down the non-competitive offer but do not have the option of participating in the auction.

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Q-Munits.8 If any of the Mselected suppliers turns down the offer, then buyer will have to

make up the resulting shortfall at a cost ofC0 per unit. Since, in any case, the buyer acquires M

units outside of the auction itself, we refer to Mas the number of non-competitive units.

Intuitively, we might argue as follows: Increasing Mincreases the fraction of suppliers in

the auction who will lose; in other words, it increases the amount of excess supply relative to the

total supply in the auction. This may increase competition and decrease the expected auction

price. If so, and if the non-competitive suppliers accept the non-competitive offer, then the buyer

benefits from having made the non-competitive offers. Furthermore, if there is little enough

excess supply, then the expected auction price may well be high enough that non-competitive

suppliers would be willing to accept it rather than be left entirely out of the process. We will

show that increasing Mdoes decrease the expected auction price, and that if the excess supply is

small enough, then there will be a positive numberMof non-competitive suppliers such that the

non-competitive suppliers obtain a greater expected profit from accepting the offer than from

declining it. In short, in theory, there is a range of cases in which the seller can decrease cost by

making some non-competitive offers.

Before deriving our results, we need to pin down a few more details. For one, the

analysis will differ depending on when the buyer makes the non-competitive offer. We assume

that the offer is made before the suppliers know precisely what their costs will be for this

particular product. At this point, the suppliers are stochastically identical. Therefore it doesnt

much matter how the M non-competitive suppliers get selected, and for our purposes, we can

(and will) think of them as being selected randomly. However, in practice non-competitive

suppliers might be selected based on some non-monetary attributes, such as a good record for

quality or delivery reliability. Committing to a supplier prior to the auction may be used as a

signal by the buyer that he is committed to a long-term relationship.

As we already argued above, under truthful bidding, the price will be equal to the lowest

cost of any losing supplier. Specifically, this gives the following proposition:

8 Note that the above restrictions onN, Q and Mimply that N-M 2 and that N-MQ-M-1; in words, there will stillbe at least two bidders and more units than bidders, thereby assuring that there will be competition in the auction.

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Proposition 1: In our auction with N-Msuppliers competing forQ-Munits,N-Q suppliers will

lose, and the per unit price established by the auction will be the N-Qth

largest of the N-M

competing suppliers costs.

Proof: This follows immediately from truthful bidding being the dominant strategy.

In addition, assume that the suppliers privately-known costs are independent draws from some

known, continuous, cumulative distribution F(.). Except for the fact that our bidders are

providing rather than acquiring goods, this is the Vickrey 1961 model with independently drawn,

privately-known values, and we henceforth refer to it as the case of IPV. As a result, there is zero

probability that two or more suppliers have exactly the same cost, and therefore truthful bidding

results in there being zero probability that more than Q suppliers are willing to provide a unit at

the final price.

Now we are ready to derive our main results. We start by noting that what really matters

is how the expected values of certain order statistics compare. Specifically, let C(i,k) (with

1ik) denote the i-th largest out of k independent samples9

and E(i,k) the expected value

E[C(i,k)]. As we observed before, the expected price established by the auction is the N-Qth

largest ofN-Msuppliers costs. Therefore, the expected auction price may be written as E(N-Q,

N-M). And if the buyer offers few enoughfew enough may be zeronon-competitive units

so that all non-competitive offers will be accepted, then the buyers expected price per unit may

also be written asE(N-Q,N-M). So, the buyer cares about howE(N-Q,N-M) varies with M.

Furthermore, a non-competitive supplier has a greater expected profit from accepting

rather than declining the offer wheneverE(N-Q, N-M) exceeds the suppliers expected cost. A

non-competitive suppliers expected cost is equal to the mean of the distribution. Note that the

mean of a distribution can be viewed as the expected value of the largest of one sample from that

distribution, which may be written asE(1,1). So an expected profit maximizing non-competitive

supplier cares about howE(1,1) compares toE(N-Q,N-M).

Our results follow from the following three basic properties of order statistics (see, for

example, Arnold, et al. 1992):

9 Actually, these results on order statisticsand their corollarieshold more generally. For example, let denotesome (unknown) underlying state of Nature and assume that the Cis are independent draws from some conditionaldistributionF(c|). Then our results hold for each possible , and since we are interested in averages, they also holdunconditionally for such conditionally independent costs Ci.

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Property 1:E(i,k) increases as kincreases.

Property 2:E(i,k) decreases as i increases.

Property 3: IfF(.) is such that ( )E median mean , then ( ) ( )/ 2 , 1,1E k k E > . For

example, if the distributionFis symmetric, then

( ) ( )/ 2 , 1,1E k k E >

.

Now we can show that the buyer benefits when suppliers provide units non-competitively.

Specifically, we have the following proposition:

Proposition 2 (Corollary to Property 1): The biggerM, the lower the expected price established

by the auction, and therefore, the lower the buyers expected cost per unit so long as all Mnon-

competitive suppliers accept the non-competitive offer.

Proof: Property 1 implies that E(N-Q, N-(M-1)) > E(N-Q, N-M), and therefore that the buyers

expected costE(N-Q,N-M) decreases as Mincreases.

So, the buyer benefits from procuring units non-competitively IF suppliers are willing to accept

non-competitive offers. But under what conditions might the suppliers be willing to provide units

non-competitively? The following two propositions address this question:

Proposition 3 (Corollary to Property 1): IfN 3, Q is close enough to N, and M= 1, then thenon-competitive contract has positive expected value, and an expected profit maximizing

supplier may be presumed to accept the contract.

Proof: ConsiderQ =N-1. Then up toN-2 contracts can be offered non-competitively andN-2

1. ForQ =N-1, we have thatN-Q = 1, and thereforeE(N-Q,N-M) =E(1,N-M). By Property 1,

E(1,N-M) >E(1,1), and thereforeE(N-Q,N-M) E(1,1) > 0.

This proposition assures that if there is little enough excess supply, then a single non-competitive

contract has positive expected value regardless of the suppliers cost distribution. But what if the

buyer wants substantially less than almost all of the available supply? Or what if the buyer wants

to offer more than one non-competitive contract? In general, the non-competitive contract may

no longer have positive expected profit to the supplier. However, the next proposition shows

that there are many distributions for which non-competitive contracts will have positive value

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even if the buyer wants substantially less than almost all of the available supply and/or offers

more than one non-competitive contract.

Proposition 4 (Corollary to Properties 2 and 3): A) If the mean cost is at most equal to the

expected median cost and 0 < M2Q-N, then the Mnon-competitive contracts have positive

expected value, and expected profit maximizing suppliers may be presumed to accept the

contracts. B) If the mean cost is equal to the expected median cost and M = 2Q-N+1 then the M

non-competitive contracts have zero expected value. C) If the mean cost is at least equal to the

expected median cost and 2Q-N+2M < N, then the Mnon-competitive contracts have negative

expected value, and expected profit maximizing suppliers may be presumed to decline the

contracts.

Proof: A) First, the hypothesized condition M2QNimplies that 2Q-2NM-N, and therefore

thatN-Q . Second, the condition N-Q( ) / 2N M ( ) / 2N M together with Property 2

implies that E(N-Q, N-M) . Finally, Property 3 implies that

>E(1,1). ThereforeE(N-Q,N-M) E(1,1) > 0. B) This follows

directly from the fact that in this case, the price setting bid in the auction is the median bid. C)

This proof is simply the mirror image of that for part A).

( )( / 2 ,E N M N M )

)( )( / 2 ,E N M N M

Note that the condition 0 < M2Q-Nimplies that Q > N/2. So, if the mean cost is less

than or equal to the expected median cost and the buyer wants just over half the available supply,

then a single non-competitive contract will have positive expected value to the supplier. And the

more that the buyers demand exceeds half of the available supply, the greater the number of

non-competitive contracts that can be offered without them becoming unprofitable to the

suppliers. In particular, if there is only one unit of excess supply, (ie Q = N-1) then the non-

competitive contracts will have positive expected value to the suppliers so long as M < Q, i.e. so

long as the buyer auctions at least one unit.

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For symmetric distributions, the expected value of the median equals the mean and

therefore the relationship holds in each of the three parts to Proposition 4. This gives the

following result:

Proposition 5 (Corollary to Proposition 4): For any symmetric distributionF, the expected value

of the contract will be positive if and only if and M < 2Q-N+1, zero if and only ifM = 2Q-N+1,

and negative if and only ifM > 2Q-N+1. In short, the expected value of the contract will have

the same sign as M (2Q-N+1).

Unlike Proposition 3, Proposition 4 does require that the distribution Fsatisfies certain

restrictions. In particular, Part A of Proposition 4 requires that the mean cost is less than the

expected median cost. However, many distributions satisfy this condition (such as all symmetric

distributions; in general, more than half of all theoretically possible cost distributions satisfy the

condition).

Furthermore, the condition may well be satisfied by real suppliers actual cost

distributions. In particular, imagine that there is some standard source or technology that puts an

upper limit on suppliers costs. Than suppliers usually cant do much better than this limit, but

occasionally a supplier may discover a superior technology, that would lower this suppliers

costs. In this case, most of the probability is concentrated near the upper end of the distribution,

with the rest scattered at lower values, and the necessary condition will hold. In this case, since

the buyer wants to have as many non-competitive sales as possible, we know exactly the number

of non-competitive contracts that should be offered. Indeed, combining propositions 2 and 4

immediately gives the following result:

Proposition 6 (Corollary to Propositions 2 and 4): If the mean cost is at most equal to the

expected median cost, the hybrid mechanism that minimizes the buyers cost is with M = 2Q-N

non-competitive sales.

As with optimal reservation prices (see for example Myerson, 1981), non-competitive

purchases destroy efficiency. There are several different ways to define efficiency. We calculate

how efficient our mechanism with non-competitive sales is in terms of the probability of an

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efficient allocation. Specifically, define PM = probability that the mechanism with M non-

competitively priced units yields an efficient allocation, and define the relative efficiency for

mechanisms with M1 and M2 non-competitive sales by1 2/ M

P .

The auction always allocates its units efficiently. Therefore,P0

= 1. And when M> 1,

the question becomes How likely is it that the Mnon-competitive suppliers are all from the set

of suppliers with the Q lowest costs (assuming that the non-competitive suppliers are chosen at

random)? This is a straight forward combinatorial question.10 In particular, the number of ways

to chose Mout ofQ is Q! / (M! (Q-M)!) and the number of ways to chose Mout ofNisN! / (M!

(N-M)!). Therefore, PM = Q! (N-M)! / (N! (Q-M)!). (Note that if M=0, then this expression

equals 1, as it should.)

3. Design of the Experiment

Our design compares the performance of the non-competitive sales mechanism (NC) and

a uniform-price descending-bid oral auction mechanism (AU) in the procurement setting. The

bidders play the roles of suppliers, and the auctioneer is the buyer who wishes to minimize the

total cost of procuring two units. Three suppliers (who together have the capacity to produce

three units) compete for the right to supply the commodity to the buyer. So in our experimental

setting,N= 3, Q = 2, and M= 1.

Suppliers have costs that are drawn randomly from a uniform distribution from zero to

100 tokens (rounded up to the nearest integer), so Fis U(0,100). The buyer also has an outside

option of purchasing units at a cost of 100 tokens (the highest possible cost). In the AU

treatment the price starts at 100 tokens and goes down by one token every second. When the

price becomes too low and a bidder wishes to stop bidding he clicks the Stop button. As soon

as one of the bidders stops bidding, the total supply falls from three to two units, and the auction

ends at the price at which the bidder dropped out. The two remaining bidders each supply one

unit and earn the difference between the auction price and their own cost.In the NC treatment one of the three bidders is randomly selected and given an option to

supply one unit at the price to be determined by the auction in which the other two bidders

compete. The bidder has to make a decision before he learns his cost in this round; he can

10 Under our assumptions, there is zero probability of two (or more) suppliers having exactly the same cost, andtherefore there is only one set of suppliers that is efficient.

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They also saw similar information about auction prices that included:

Auction prices that resulted in each market Average price in each market Average price each period Average price across all markets and all periods.Figure 1 displays the actual information that participants in the non-competitive treatment saw at

the end of the ten practice rounds.

Figure 1. Summary information shown to participants at the end of the ten practice periods in the non-competitivesales treatment.

We used a random number generator in Microsoft Excel to draw the costs, and for the practice

rounds we selected a sample of draws that resulted in overall average cost of close to 50 (51.07in actuality) and an overall average auction price, assuming that all bidders follow the dominant

bidding strategy, of close to 66.7 (the actual prices varied slightly by session, since participants

deviated slightly from the dominant bidding strategy, especially in early rounds). The purpose of

providing this summary information was to promote faster understanding on the part of the

participants in the NC treatment about what the average costs and auction prices are likely to be.

The practice rounds were also conducted in the AU treatment for the purpose of keeping the

experimental protocol as similar as possible in the two treatments.

Starting in period 11, the participants played the 30 rounds of the game. Each round in

both treatments started with the summary information similar to Figure 1 (but also including

information for all previous rounds). In the NC treatment one of the three suppliers was also

asked to decide whether to accept or decline the option to supply one unit at the end of the

auction at the auction price. The other two suppliers in the NC treatment, as well as all three

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suppliers in the AU treatment, simply had a Continue button on their screen. The round then

proceeded to the auction. After the auction all suppliers learned the outcome of the current

round that included:

A reminder of what they did in this round (either bid in the auction, supplied a unit after theauction, or did not participate)

Cost this round Auction price Profit.Additionally, in the NC treatment the non-competitive supplier was told what his profit would

have been had he made a decision that was different from the one he actually made. So if the

supplier opted to not supply the unit, he was told the profit or loss he would have made had he

decided to supply it, and if the supplier opted to supply the unit, he was told that had he decided

not to supply the unit he would have earned zero. See the Appendix for complete instructions.

All sessions were conducted at Penn States Smeal College of Business Laboratory for

Economic Management and Auctions (LEMA) on June 1 and 2, 2004. Participants, mostly

undergraduate students from diverse fields of study, were recruited using the on-line recruitment

system. Cash was the only incentive offered. Participants were paid their total individual

earnings from all 40 rounds (ten practice rounds and 30 actual rounds) plus a $5 show-up fee at

the end of the session. The software was built using the zTree system (Fischbacher 1999). Each

session lasted about 90 minutes and average earnings were approximately $25 in the AUtreatment and $24 in the NC treatment.

4. Results

4.1 Non-competitive Suppliers Decisions

The critical assumption of our theory is that the non-competitive supplier should decide to accept

the option to supply one unit after the auction at the price determined by the auction. Expected

profit from accepting the option is positive, so if the suppliers objective is simply to maximize

their expected profit, then they should always accept the option. Figure 2 shows the actual

average acceptance rates over time in all six sessions.

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0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Period

PercentageeIN

(a) Proportion of suppliers opting in of all six sessions over time

0%

10%

20%

30%

40%

50%

60%

70%

80%90%

100%

11 - 20 21 - 30 31 - 40

Periods

ProportionIn

Session 1 Session 2 Session 3 Session 4 Session 5 Session 6

(b) Proportion of suppliers opting in, grouped in blocks of ten periods broken out by session.

Figure 2. Actual average Proportion of suppliers opting in for all six sessions over time.

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Session Subject Periods in Periods out Comments

1 1 1 - 10 none always in (A)

2 1 - 10 none always in (A)3 1,2,6,9 3,4,5,7,8,10 First out after a large profit (59), subsequent outs after a loss (M)4 1 - 6,8,10 7,9 First out after first loss, second out after a large win (76) (M)

5 1,2,3,5 - 10 4

One out after a small win (3) that followed a large loss (71).

Subsequently all wins (A)6 1,2,10 3 - 9 Out following 2 losses in a row. No gain experience (L)

2 1 1,3,4,7,8 2,5,6,9,10

First out following a large loss (-66); second out following alarge loss (-80) followed by a large gain (91), subsequent outsfollowing a small gain (13) that followed a small loss (-17) (M)

2 1,2,5,7,8,10 3,4,6,9First out following 2 losses, next out following a loss, last outfollowing a large (86) gain (M)

3 1 - 7 8 - 10 Out following a small gain (9) that followed a small loss (-4)

4 1,2,6,8 2,4,5,7,9,10First 2 outs followed a large gain (60 and 56) and last followed amedium gain (26) (G)

5 1 - 6, 8 - 10 7 Out followed a loss (-19) (A)

6 1 - 4, 7 5,6,8 - 10First out followed a gain of 0 that followed a large loss (-62);second out followed a large gain (55) (M)

3 1 1 - 10 none always in (A)

2 1 - 10 none always in (A)




6 1-3,5-10 4 Out followed a loss (32) (A)

4 1 1 - 4,8 - 10 5,6,7 out followed a large gain (41) (G)

2 1,4,5,7 - 10 2,3,6Out in period 1, next 2 outs followed a medium (22) and a large(47) gain (G)

3 1 - 5,7 - 9 6,10Out followed a large gain (74), out last time following a smallgain (15)


5 1,4,5,10 2,3,6 - 9First out followed a small loss (-9) and second out followed alarge gain (97) (M)

6 1 - 5,7,9,20 6,8 Outs followed a loss (L)

5 1 1 - 7, 9,10 8 no reason (A)2 2 1, 3 - 10 out in period 1 and following a loss. No gain experience (L)

3 1,2,5,7,8,9 3,4,6,10First out followed a loss (-33), second after a gain of 0, last inperiod 10

4 1,3 - 6,9,10 2,7,8First out followed a small loss (-6) and second followed a largegain (33) (M)

5 1 - 8 9,10 Out followed a large gain (56) (G)6 1 - 4,7 - 10 5,6 Out following a small gain (14) that followed a large gain (64)

6 1 1 - 6, 8 - 10 7 One out followed a large gain (A)

2 1 - 10 none always in (A)3 1 - 10 none always in (A)




Table 2. Summary of individual behavior of non-competitive suppliers

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Acceptance rates start out at 100% decrease over the first 10 periods, and then settle down at

about 70%. The actual average acceptance rate in periods 11 20 is 89%, in period 21 30 it is

71.6% (the decrease from 89.1% to 71.7% is statistically significant; one-sided matched-pair t-

test p-value is 0.0106). The average acceptance rate in periods 31 40 is 70% (the decrease

from 71.7% to 70% is not statistically significant; one-sided matched-pair t-test p-value is

0.3856). Note some heterogeneity among the sessions: acceptance rate is nearly 100%

throughout in sessions 3 and 6, is only 60% in session 2, and close to 70% in the other three

sessions.

The initial high acceptance rate and the initial fall is not surprising: Recall that in periods

1 10 participants experience the outcomes of an ascending auction with two bidders and one

object, and observe information about costs and prices. By the end of period 10 the average

actual costs are close to the theoretical average of 50, and the average actual auction price is

close to the theoretical average of 66.7. The fact that acceptance rates are close to 100% early on

is evidence that participants are able to process the average cost and price information correctly,

and determine that accepting the non-competitive contract is profitable on average. To obtain a

clearer picture of how individuals make decisions to accept or to decline non-competitive

contracts, we summarize individual decisions in Table 2.

Of the 36 subjects, 18 (50%) either always accept the contract, or reject it one time only

one time (we classify them as A in Table 2). Of the remaining 18 subjects, 14 (78%) reject the

contract either following a loss of following a large gain (for the purpose of this analysis, we

conservatively classify a gain as being large when it is over 20the average expected gain from

accepting the contract is 66.7 50 = 16.7). Rejecting the contract after a loss can be explained by

loss aversion, while rejecting it after a large gain is the common quit while ahead strategy.

There appears to be a fairly common pattern, marked M in Table 2, that involves rejecting the

contract after either a loss or a large gain, and often the same participant does both (subjects 3

and 4 in session 1, subjects 1, 2 and 6 in session 2, subject 5 in session 4, and subject 4 in session

5seven subjects in total). The rest of the subjects, marked L(oss) and G(ain) in Table 2,

reject the contract either only after a loss (subject 6 in session 1, subject 6 in session 4, subject 2

in session 5three subjects) or only after a large gain (subject 4 in session 2, subjects 1 and 2 in

session 4, and subject 5 in session 5four subjects). The remaining four subjects reject the

contract after a small or medium gain: subject 3 in session 2 opted out after a small gain that

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followed a loss, subject 3 in session 2 opted one time after a large gain of 74 and the second time

after a gain of 15, subject 3 in session 5 opted out one time after a loss, then again after a gain of

zero, and last time in period 10, and subject 6 in session 5 opted out the first time after a gain of

14, and the second time after a large gain of 64.

The main point is that the acceptance rate, after the initial decrease, settles down and

stays fairly constant at about 70% in the last 20 rounds of the game (or after the initial ten

rounds). Therefore, we will confine the rest of our analysis to the last 20 rounds of the gamea

period where acceptance rates have reached a constant level.

4.2 Bidding Behavior

The second presumption of the theory is that bidders follow the dominant bidding strategy in the

auction. It has been well-established that participants are able to learn to bid close to the

dominant strategy in ascending auctions (see Kagel 1995 and references therein). Our

experiment differs from the standard setting because we use the reverse auction frame, and in

that (in the AU treatment) two units are auctioned off. We plot bids as a function of cost in

Figure 3.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Cost

Bid

Figure 3. Bid as a function of cost

Despite the differences between our setting and the standard experimental setting, the

bidding behavior is very close the dominant strategy in both treatments. Overall, 66% of the bids

exactly equal cost (68% in the AU treatment and 65 in the NC treatment), and 89% of the bids

are within five tokens of cost (87% in the AU treatment and 90% in the NC treatment). About

9.5% of the bids are more than five tokens above cost (10.9% in the AU treatment and 8% in the

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NC treatment) and about 2% of the bids are more than five tokens below cost (1.7% in the AU

treatment and 2.3% in the NC treatment).

Since a bid that is below cost might result in a loss, bids below cost are clearly errors, and

we see very few of them (only 2%). Bids that are slightly above cost indicate that a bidder

dropped out before the price reached the cost, so those bids can potentially result in foregoing an

opportunity to win the auction, and might indicate an attempt on the part of some of the bidders

to collude by driving the overall price level down. This tendency indicates that actual auction

prices are slightly above those predicted by the theory. However, since the tendency to drop out

early is small, and is approximately the same in both treatments, it should not have a significant

effect on the differences in total costs between the two treatments.

4.3 Efficiency Comparisons

In theory the AU mechanism is 100% efficient, and the NC mechanism is only 67%

efficient, because when the high cost supplier is selected for the noncompetitive contract, the

mechanism must result in an inefficient allocation. In the experiment, about 91% of the auctions

resulted in the efficient allocation in the AU treatment, but only 48% in the NC treatment.

Figure 4 summarizes the causes of inefficiencies in the 2 treatments.

0%

10%

20%

30%

40%

50%

60%

AU NC

Treatment

Proportionofinefficient

allocatio

Auction outcome Hich cost chosen Low cost opt out

Figure 3. Causes of inefficiency

The auction outcome itself is not 100% efficient because bidders occasionally stop

bidding short of their costs, and this causes 31 out of 360 auctions (about 9%) in the AU

treatment to result in inefficient allocations. In the NC treatment, only ten out of 360 auctions

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result in inefficient auction allocations (about 3%), but the two major sources of inefficiency are

(1) the high cost supplier being chosen for the non-competitive contract (which, by design,

happened in 33% of the auctions), and (2) a low cost supplier was chosen for the non-

competitive contract, but rejected the contract (this happened in 57 out of 360 auctionsabout

16%11).

.

4.4 Buyer Cost Comparison

We summarize the actual and predicted buyer costs grouped in ten period blocks in Table 3, and

display this information for the last 20 periods graphically in Figure 4.

PredictedPeriods 11 - 20 Periods 21 - 30 Periods 31 40 All Periods

Session AU NC AU NC AU NC AU NC1 159.4 142.5 141.3 123.2 139.4 132.9 146.7 132.9

2 151.2 121.8 153.8 138.9 147.9 131.0 150.9 130.63 130.0 114.1 161.7 147.7 156.5 134.2 149.4 132.04 148.0 140.4 155.6 132.0 148.2 130.0 150.6 134.15 149.8 136.6 146.8 133.9 139.5 130.0 145.4 133.56 152.1 136.5 158.4 142.0 132.3 114.2 147.6 130.9

Avera e 148.4 132.0 152.9 136.3 144.0 128.7 148.4 132.3ctual

Periods 11 - 20 Periods 21 - 30 Periods 31 40 All PeriodsSession AU NC AU NC AU NC AU NC

1 170.4 147.5 144.5 135.0 141.1 138.4 152.0 140.32 155.2 128.6 161.9 148.8 155.9 148.7 157.7 142.03 132.2 115.3 168.4 148.9 159.2 133.8 153.3 132.74 149.9 141.8 161.2 150.6 154.0 146.8 155.0 146.45 157.0 144.4 152.8 146.0 144.9 149.2 151.6 146.5

6 157.2 142.4 159.9 148.6 137.4 134.7 151.5 141.9Average 153.7 136.6 158.1 146.3 148.8 141.9 153.5 141.6

Table 3. Summary of the predicted and actual total buyer cost.

11 We count this latter case as an inefficiency, although in practice a supplier who rejected a non-competitivecontract may have some more attractive outside options, and therefore the actual outcome may not be inefficient

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125.0

130.0

135.0

140.0

145.0

150.0

155.0

160.0

165.0

1 2 3 4 5 6

Session

AverageC

ost

AU NC

Average CostsAU:

Predicted: 148.5Actual: 153.4Difference: 5.0 (3.25%) p-value: 0.2356

NC:Predicted: 144.1Actual: 132.5Difference: 11.6 (8.05%) p-value: 0.0041

Difference between AU and NC:Predicted: 16.0 (10.7%) p-value: 0.0026

Actual: 9.3 (6.1%) p-value: 0.0153

Figure 4. Actual and predicted average costs for all 30 periods (periods 21 40 in the study), broken out bysessions. The p-values refer to one-sided Mann-Whitney U test (Wilcoxon test) with the null hypothesis of MC

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Theory and Behavious in Reverse Auctions